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      <a href="/2017/08/04/n-n-matrix/" title="算法导论之js实现--n×n矩阵计算" itemprop="url">算法导论之js实现--n×n矩阵计算</a>
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      <a href="https://godbasin.github.io" title="被删">被删</a>
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    <time datetime="2017-08-04T14:51:57.000Z" itemprop="datePublished">2017-08-04</time>
    更新日期:<time datetime="2018-08-18T12:58:12.540Z" itemprop="dateModified">2018-08-18</time>
    
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			<strong class="toc-title">文章目录</strong>
		<ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#n×n矩阵计算"><span class="toc-number">1.</span> <span class="toc-text">n×n矩阵计算</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#n×n矩阵"><span class="toc-number">1.1.</span> <span class="toc-text">n×n矩阵</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#基本js实现"><span class="toc-number">1.2.</span> <span class="toc-text">基本js实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证"><span class="toc-number">1.3.</span> <span class="toc-text">验证</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#分治策略的矩阵算法"><span class="toc-number">2.</span> <span class="toc-text">分治策略的矩阵算法</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#直接的递归分治算法"><span class="toc-number">2.1.</span> <span class="toc-text">直接的递归分治算法</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#矩阵乘法的Strassen算法"><span class="toc-number">2.2.</span> <span class="toc-text">矩阵乘法的Strassen算法</span></a></li></ol></li></ol>
		</div>
		
		<p>n×n矩阵计算的javascript实现。<br><a id="more"></a></p>
<h2 id="n×n矩阵计算"><a href="#n×n矩阵计算" class="headerlink" title="n×n矩阵计算"></a>n×n矩阵计算</h2><hr>
<h3 id="n×n矩阵"><a href="#n×n矩阵" class="headerlink" title="n×n矩阵"></a>n×n矩阵</h3><p>若<code>A = (a[i][j])</code>和<code>B = (b[i][j])</code>为n × n的方阵，则对<code>i, j = 1, 2, ..., n</code>，定义乘积<code>C = A · B</code>中的元素<code>c[i][j]</code>为：</p>
<p><img src="https://github-imglib-1255459943.cos.ap-chengdu.myqcloud.com/1487758346%281%29.png" alt="image"></p>
<h3 id="基本js实现"><a href="#基本js实现" class="headerlink" title="基本js实现"></a>基本js实现</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">squareMatrixMultiply</span>(<span class="params">A, B</span>) </span>&#123;</div><div class="line">    <span class="keyword">var</span> n = A.length;</div><div class="line">    <span class="keyword">var</span> C = [];</div><div class="line">    <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123;</div><div class="line">        C[i] = [];</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; n; j++) &#123;</div><div class="line">            C[i][j] = <span class="number">0</span>;</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> k = <span class="number">0</span>; k &lt; n; k++) &#123;</div><div class="line">                C[i][j] += A[i][k] * B[k][j];</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">return</span> C;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<h3 id="验证"><a href="#验证" class="headerlink" title="验证"></a>验证</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>], [<span class="number">7</span>, <span class="number">5</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>], [<span class="number">4</span>, <span class="number">2</span>]];</div><div class="line">squareMatrixMultiply(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[18, 14], [62, 66]]</span></div><div class="line"></div><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>, <span class="number">2</span>, <span class="number">1</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>], [<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">9</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>, <span class="number">2</span>, <span class="number">2</span>], [<span class="number">4</span>, <span class="number">2</span>, <span class="number">2</span>, <span class="number">8</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>]];</div><div class="line">squareMatrixMultiply(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[29, 25, 11, 37], [113, 104, 32, 105], [83, 66, 18, 87], [40, 35, 13, 44]]</span></div></pre></td></tr></table></figure>
<h2 id="分治策略的矩阵算法"><a href="#分治策略的矩阵算法" class="headerlink" title="分治策略的矩阵算法"></a>分治策略的矩阵算法</h2><hr>
<h3 id="直接的递归分治算法"><a href="#直接的递归分治算法" class="headerlink" title="直接的递归分治算法"></a>直接的递归分治算法</h3><ul>
<li>思路</li>
</ul>
<p><img src="https://github-imglib-1255459943.cos.ap-chengdu.myqcloud.com/1487758627%281%29.png" alt="image"></p>
<ul>
<li>js实现</li>
</ul>
<figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div><div class="line">77</div><div class="line">78</div><div class="line">79</div><div class="line">80</div><div class="line">81</div><div class="line">82</div><div class="line">83</div><div class="line">84</div><div class="line">85</div><div class="line">86</div><div class="line">87</div><div class="line">88</div><div class="line">89</div><div class="line">90</div><div class="line">91</div><div class="line">92</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">squareMatrixMultiplyRecursive</span>(<span class="params">A, B</span>) </span>&#123;</div><div class="line">    <span class="comment">// 传入原矩阵、复制起点(x, y)、复制长度n</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">getMatrix</span>(<span class="params">M, x, y, n</span>) </span>&#123;</div><div class="line">        <span class="comment">// console.log(M, x, y, n)</span></div><div class="line">        <span class="keyword">var</span> N = [];</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123;</div><div class="line">            N[i] = [];</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; n; j++) &#123;</div><div class="line">                <span class="comment">// 复制值</span></div><div class="line">                N[i][j] = M[i + y][j + x];</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">return</span> N;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="comment">// 方阵的相加, 若传入type为'minus'，则进行减运算</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">addMatrix</span>(<span class="params">A, B, type</span>) </span>&#123;</div><div class="line">        <span class="keyword">var</span> n = A.length;</div><div class="line">        <span class="keyword">var</span> N = [];</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123;</div><div class="line">            N[i] = [];</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; n; j++) &#123;</div><div class="line">                <span class="comment">// 复制值</span></div><div class="line">                N[i][j] = type === <span class="string">'minus'</span> ? (A[i][j] - B[i][j]) : (A[i][j] + B[i][j]);</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">return</span> N;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="comment">// 整理矩阵，将多维数组整理成二维数组</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">convertMatrix</span>(<span class="params">M</span>) </span>&#123;</div><div class="line">        <span class="comment">// 取出所有值</span></div><div class="line">        <span class="keyword">var</span> arr = M.toString().split(<span class="string">','</span>);</div><div class="line">        <span class="keyword">var</span> array = [];</div><div class="line">        <span class="comment">// 选出有效值</span></div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> k = <span class="number">0</span>; k &lt; arr.length; k++) &#123;</div><div class="line">            <span class="keyword">if</span> (arr[k]) &#123; array.push(<span class="built_in">Number</span>(arr[k])); &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="comment">// 计算数组长度以及平方根</span></div><div class="line">        <span class="keyword">var</span> n = array.length;</div><div class="line">        <span class="keyword">var</span> m = <span class="built_in">Math</span>.sqrt(n);</div><div class="line">        <span class="comment">// console.log('M', M, n, m)</span></div><div class="line"></div><div class="line">        <span class="comment">// 重新整理为二维数组</span></div><div class="line">        <span class="keyword">var</span> N = [], L = [];</div><div class="line">        N[<span class="number">0</span>] = array.slice(<span class="number">0</span>, n / <span class="number">4</span>);</div><div class="line">        N[<span class="number">1</span>] = array.slice(n / <span class="number">4</span>, n / <span class="number">2</span>);</div><div class="line">        N[<span class="number">2</span>] = array.slice(n / <span class="number">2</span>, n * <span class="number">3</span> / <span class="number">4</span>);</div><div class="line">        N[<span class="number">3</span>] = array.slice(n * <span class="number">3</span> / <span class="number">4</span>, n);</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; m; i++) &#123;</div><div class="line">            L[i] = [];</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> l = <span class="number">0</span>; l &lt; <span class="number">4</span>; l++) &#123;</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; m / <span class="number">2</span>; i++) &#123;</div><div class="line">                <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; m / <span class="number">2</span>; j++) &#123;</div><div class="line">                    L[i + <span class="built_in">Math</span>.floor(l / <span class="number">2</span>) * m / <span class="number">2</span>].push(N[l][j + i * m / <span class="number">2</span>]);</div><div class="line">                &#125;</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">return</span> L;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="keyword">var</span> n = A.length;  <span class="comment">// 获取长度</span></div><div class="line">    <span class="comment">// 创建n×n矩阵C</span></div><div class="line">    <span class="keyword">var</span> C = [];</div><div class="line">    <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123; C[i] = []; &#125;</div><div class="line">    <span class="keyword">if</span> (n === <span class="number">1</span>) &#123;</div><div class="line">        <span class="comment">// 若只有一个数，则返回乘积</span></div><div class="line">        C[<span class="number">0</span>][<span class="number">0</span>] = A[<span class="number">0</span>][<span class="number">0</span>] * B[<span class="number">0</span>][<span class="number">0</span>];</div><div class="line">    &#125; <span class="keyword">else</span> &#123;</div><div class="line">        <span class="keyword">var</span> m = <span class="built_in">parseInt</span>(n / <span class="number">2</span>);</div><div class="line">        <span class="comment">// 分割A为n/2矩阵[[A11, A12], [A21, A22]]</span></div><div class="line">        <span class="keyword">var</span> A11 = getMatrix(A, <span class="number">0</span>, <span class="number">0</span>, m);</div><div class="line">        <span class="keyword">var</span> A12 = getMatrix(A, m, <span class="number">0</span>, n - m);</div><div class="line">        <span class="keyword">var</span> A21 = getMatrix(A, <span class="number">0</span>, m, n - m);</div><div class="line">        <span class="keyword">var</span> A22 = getMatrix(A, m, m, m);</div><div class="line">        <span class="comment">// 分割B为n/2矩阵[[B11, B12], [B21, B22]]</span></div><div class="line">        <span class="keyword">var</span> B11 = getMatrix(B, <span class="number">0</span>, <span class="number">0</span>, m);</div><div class="line">        <span class="keyword">var</span> B12 = getMatrix(B, m, <span class="number">0</span>, n - m);</div><div class="line">        <span class="keyword">var</span> B21 = getMatrix(B, <span class="number">0</span>, m, n - m);</div><div class="line">        <span class="keyword">var</span> B22 = getMatrix(B, m, m, m);</div><div class="line"></div><div class="line">        <span class="comment">// 递归求出A11, A12, A21, A22以及B11, B12, B21, B22的值</span></div><div class="line">        <span class="comment">// 求出矩阵C，并返回</span></div><div class="line">        C[<span class="number">0</span>][<span class="number">0</span>] = addMatrix(squareMatrixMultiplyRecursive(A11, B11), squareMatrixMultiplyRecursive(A12, B21));</div><div class="line">        C[<span class="number">0</span>][<span class="number">1</span>] = addMatrix(squareMatrixMultiplyRecursive(A11, B12), squareMatrixMultiplyRecursive(A12, B22));</div><div class="line">        C[<span class="number">1</span>][<span class="number">0</span>] = addMatrix(squareMatrixMultiplyRecursive(A21, B11), squareMatrixMultiplyRecursive(A22, B21));</div><div class="line">        C[<span class="number">1</span>][<span class="number">1</span>] = addMatrix(squareMatrixMultiplyRecursive(A21, B12), squareMatrixMultiplyRecursive(A22, B22));</div><div class="line">        C = convertMatrix(C);</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">return</span> C;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<ul>
<li>验证</li>
</ul>
<figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>], [<span class="number">7</span>, <span class="number">5</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>], [<span class="number">4</span>, <span class="number">2</span>]];</div><div class="line">squareMatrixMultiplyRecursive(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[18, 14], [62, 66]]</span></div><div class="line"></div><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>, <span class="number">2</span>, <span class="number">1</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>], [<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">9</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>, <span class="number">2</span>, <span class="number">2</span>], [<span class="number">4</span>, <span class="number">2</span>, <span class="number">2</span>, <span class="number">8</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>]];</div><div class="line">squareMatrixMultiplyRecursive(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[29, 25, 11, 37], [113, 104, 32, 105], [83, 66, 18, 87], [40, 35, 13, 44]]</span></div></pre></td></tr></table></figure>
<h3 id="矩阵乘法的Strassen算法"><a href="#矩阵乘法的Strassen算法" class="headerlink" title="矩阵乘法的Strassen算法"></a>矩阵乘法的Strassen算法</h3><p>该算法比较长，大家可参考《算法导论》一书或者<a href="https://ccjou.wordpress.com/2013/06/04/%E5%88%86%E6%B2%BB%E7%9F%A9%E9%99%A3%E4%B9%98%E6%B3%95%E2%94%80%E2%94%80strassen-%E6%BC%94%E7%AE%97%E6%B3%95/" target="_blank" rel="external">Strassen 演算法──分治矩陣乘法</a>。</p>
<ul>
<li>思路</li>
</ul>
<p>2×2矩阵计算：<br><img src="https://github-imglib-1255459943.cos.ap-chengdu.myqcloud.com/latex.png" alt="image"></p>
<p>传统的矩阵乘法运算方式，<code>C[i][j] = A[i][1]·B[1][j] + A[i][2]·B[2][j]</code>，总共使用8个分块乘法和4个分块加法。<br>Strassen演算使用7个分块乘法和18个分块加法：<br><img src="https://github-imglib-1255459943.cos.ap-chengdu.myqcloud.com/latex%20%281%29.png" alt="image"></p>
<ul>
<li>js实现</li>
</ul>
<figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div><div class="line">77</div><div class="line">78</div><div class="line">79</div><div class="line">80</div><div class="line">81</div><div class="line">82</div><div class="line">83</div><div class="line">84</div><div class="line">85</div><div class="line">86</div><div class="line">87</div><div class="line">88</div><div class="line">89</div><div class="line">90</div><div class="line">91</div><div class="line">92</div><div class="line">93</div><div class="line">94</div><div class="line">95</div><div class="line">96</div><div class="line">97</div><div class="line">98</div><div class="line">99</div><div class="line">100</div><div class="line">101</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">squareMatrixMultiplyStrassen</span>(<span class="params">A, B</span>) </span>&#123;</div><div class="line">    <span class="comment">// 传入原矩阵、复制起点(x, y)、复制长度n</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">getMatrix</span>(<span class="params">M, x, y, n</span>) </span>&#123;</div><div class="line"></div><div class="line">        <span class="keyword">var</span> N = [];</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123;</div><div class="line">            N[i] = [];</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; n; j++) &#123;</div><div class="line">                <span class="comment">// 复制值</span></div><div class="line">                N[i][j] = M[i + y][j + x];</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="comment">// console.log(M,x,y,n,N)</span></div><div class="line">        <span class="keyword">return</span> N;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="comment">// 方阵的相加, 若传入type为'minus'，则进行减运算</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">addMatrix</span>(<span class="params">A, B, type</span>) </span>&#123;</div><div class="line">        <span class="keyword">var</span> n = A.length;</div><div class="line">        <span class="keyword">var</span> N = [];</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123;</div><div class="line">            N[i] = [];</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; n; j++) &#123;</div><div class="line">                <span class="comment">// 复制值</span></div><div class="line">                N[i][j] = type === <span class="string">'minus'</span> ? (A[i][j] - B[i][j]) : (A[i][j] + B[i][j]);</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">return</span> N;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="comment">// 整理矩阵，将多维数组整理成二维数组</span></div><div class="line">    <span class="function"><span class="keyword">function</span> <span class="title">convertMatrix</span>(<span class="params">M</span>) </span>&#123;</div><div class="line">        <span class="comment">// 取出所有值</span></div><div class="line">        <span class="keyword">var</span> arr = M.toString().split(<span class="string">','</span>);</div><div class="line">        <span class="keyword">var</span> array = [];</div><div class="line">        <span class="comment">// 选出有效值</span></div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> k = <span class="number">0</span>; k &lt; arr.length; k++) &#123;</div><div class="line">            <span class="keyword">if</span> (arr[k]) &#123; array.push(<span class="built_in">Number</span>(arr[k])); &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="comment">// 计算数组长度以及平方根</span></div><div class="line">        <span class="keyword">var</span> n = array.length;</div><div class="line">        <span class="keyword">var</span> m = <span class="built_in">Math</span>.sqrt(n);</div><div class="line">        <span class="comment">// console.log('M', M, n, m)</span></div><div class="line"></div><div class="line">        <span class="comment">// 重新整理为二维数组</span></div><div class="line">        <span class="keyword">var</span> N = [], L = [];</div><div class="line">        N[<span class="number">0</span>] = array.slice(<span class="number">0</span>, n / <span class="number">4</span>);</div><div class="line">        N[<span class="number">1</span>] = array.slice(n / <span class="number">4</span>, n / <span class="number">2</span>);</div><div class="line">        N[<span class="number">2</span>] = array.slice(n / <span class="number">2</span>, n * <span class="number">3</span> / <span class="number">4</span>);</div><div class="line">        N[<span class="number">3</span>] = array.slice(n * <span class="number">3</span> / <span class="number">4</span>, n);</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; m; i++) &#123;</div><div class="line">            L[i] = [];</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> l = <span class="number">0</span>; l &lt; <span class="number">4</span>; l++) &#123;</div><div class="line">            <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; m / <span class="number">2</span>; i++) &#123;</div><div class="line">                <span class="keyword">for</span> (<span class="keyword">var</span> j = <span class="number">0</span>; j &lt; m / <span class="number">2</span>; j++) &#123;</div><div class="line">                    L[i + <span class="built_in">Math</span>.floor(l / <span class="number">2</span>) * m / <span class="number">2</span>].push(N[l][j + i * m / <span class="number">2</span>]);</div><div class="line">                &#125;</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="keyword">return</span> L;</div><div class="line">    &#125;</div><div class="line"></div><div class="line">    <span class="keyword">var</span> n = A.length;  <span class="comment">// 获取长度</span></div><div class="line">    <span class="comment">// 创建n×n矩阵C</span></div><div class="line">    <span class="keyword">var</span> C = [];</div><div class="line">    <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n; i++) &#123; C[i] = []; &#125;</div><div class="line">    <span class="keyword">if</span> (n === <span class="number">1</span>) &#123;</div><div class="line">        <span class="comment">// 若只有一个数，则返回乘积</span></div><div class="line">        C[<span class="number">0</span>][<span class="number">0</span>] = A[<span class="number">0</span>][<span class="number">0</span>] * B[<span class="number">0</span>][<span class="number">0</span>];</div><div class="line">    &#125; <span class="keyword">else</span> &#123;</div><div class="line">        <span class="keyword">var</span> m = <span class="built_in">parseInt</span>(n / <span class="number">2</span>);</div><div class="line">        <span class="comment">// 分割A为n/2矩阵[[A11, A12], [A21, A22]]</span></div><div class="line">        <span class="keyword">var</span> A11 = getMatrix(A, <span class="number">0</span>, <span class="number">0</span>, m);</div><div class="line">        <span class="keyword">var</span> A12 = getMatrix(A, m, <span class="number">0</span>, n - m);</div><div class="line">        <span class="keyword">var</span> A21 = getMatrix(A, <span class="number">0</span>, m, n - m);</div><div class="line">        <span class="keyword">var</span> A22 = getMatrix(A, m, m, m);</div><div class="line">        <span class="comment">// 分割B为n/2矩阵[[B11, B12], [B21, B22]]</span></div><div class="line">        <span class="keyword">var</span> B11 = getMatrix(B, <span class="number">0</span>, <span class="number">0</span>, m);</div><div class="line">        <span class="keyword">var</span> B12 = getMatrix(B, m, <span class="number">0</span>, n - m);</div><div class="line">        <span class="keyword">var</span> B21 = getMatrix(B, <span class="number">0</span>, m, n - m);</div><div class="line">        <span class="keyword">var</span> B22 = getMatrix(B, m, m, m);</div><div class="line"></div><div class="line">        <span class="comment">// 计算7个P矩阵</span></div><div class="line">        <span class="keyword">var</span> P1 = squareMatrixMultiplyStrassen(addMatrix(A11, A22), addMatrix(B11, B22));</div><div class="line">        <span class="keyword">var</span> P2 = squareMatrixMultiplyStrassen(addMatrix(A21, A22), B11);</div><div class="line">        <span class="keyword">var</span> P3 = squareMatrixMultiplyStrassen(A11, addMatrix(B12, B22, <span class="string">'minus'</span>));</div><div class="line">        <span class="keyword">var</span> P4 = squareMatrixMultiplyStrassen(A22, addMatrix(B21, B11, <span class="string">'minus'</span>));</div><div class="line">        <span class="keyword">var</span> P5 = squareMatrixMultiplyStrassen(addMatrix(A11, A12), B22);</div><div class="line">        <span class="keyword">var</span> P6 = squareMatrixMultiplyStrassen(addMatrix(A21, A11, <span class="string">'minus'</span>), addMatrix(B11, B12));</div><div class="line">        <span class="keyword">var</span> P7 = squareMatrixMultiplyStrassen(addMatrix(A12, A22, <span class="string">'minus'</span>), addMatrix(B21, B22));</div><div class="line"></div><div class="line">        <span class="comment">// 求出矩阵C，并返回</span></div><div class="line">        C[<span class="number">0</span>][<span class="number">0</span>] = convertMatrix(addMatrix(addMatrix(P1, P4), addMatrix(P5, P7, <span class="string">'minus'</span>), <span class="string">'minus'</span>));</div><div class="line">        C[<span class="number">0</span>][<span class="number">1</span>] = convertMatrix(addMatrix(P3, P5));</div><div class="line">        C[<span class="number">1</span>][<span class="number">0</span>] = convertMatrix(addMatrix(P2, P4));</div><div class="line">        C[<span class="number">1</span>][<span class="number">1</span>] = convertMatrix(addMatrix(addMatrix(P1, P3), addMatrix(P2, P6, <span class="string">'minus'</span>), <span class="string">'minus'</span>));</div><div class="line">        C = convertMatrix(C);</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">return</span> C;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<ul>
<li>验证</li>
</ul>
<figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>], [<span class="number">7</span>, <span class="number">5</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>], [<span class="number">4</span>, <span class="number">2</span>]];</div><div class="line">squareMatrixMultiplyStrassen(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[18, 14], [62, 66]]</span></div><div class="line"></div><div class="line"><span class="keyword">var</span> AMatrix = [[<span class="number">1</span>, <span class="number">3</span>, <span class="number">2</span>, <span class="number">1</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>], [<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">9</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>]];</div><div class="line"><span class="keyword">var</span> BMatrix = [[<span class="number">6</span>, <span class="number">8</span>, <span class="number">2</span>, <span class="number">2</span>], [<span class="number">4</span>, <span class="number">2</span>, <span class="number">2</span>, <span class="number">8</span>], [<span class="number">2</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">2</span>], [<span class="number">7</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">7</span>]];</div><div class="line">squareMatrixMultiplyStrassen(AMatrix, BMatrix); </div><div class="line"><span class="comment">// 输出[[29, 25, 11, 37], [113, 104, 32, 105], [83, 66, 18, 87], [40, 35, 13, 44]]</span></div></pre></td></tr></table></figure>
<p>写着玩的，认真你就输了哈哈。</p>
  
		
		<p style="margin-top:50px;">查看Github有更多内容噢：<a href="https://github.com/godbasin">https://github.com/godbasin</a></p>
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	<p style="text-align: center;margin-top: 10px;margin-bottom: 20px;">码生艰难，写文不易，给我家猪囤点猫粮了喵~</p>
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  		<p>作者：被删</p>
  		<p>出处：<a href="https://godbasin.github.io">https://godbasin.github.io</a></p>
  		<p>本文版权归作者所有，欢迎转载，但未经作者同意必须保留此段声明，且在文章页面明显位置给出原文连接，否则保留追究法律责任的权利。</p>
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  <ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#n×n矩阵计算"><span class="toc-number">1.</span> <span class="toc-text">n×n矩阵计算</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#n×n矩阵"><span class="toc-number">1.1.</span> <span class="toc-text">n×n矩阵</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#基本js实现"><span class="toc-number">1.2.</span> <span class="toc-text">基本js实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证"><span class="toc-number">1.3.</span> <span class="toc-text">验证</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#分治策略的矩阵算法"><span class="toc-number">2.</span> <span class="toc-text">分治策略的矩阵算法</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#直接的递归分治算法"><span class="toc-number">2.1.</span> <span class="toc-text">直接的递归分治算法</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#矩阵乘法的Strassen算法"><span class="toc-number">2.2.</span> <span class="toc-text">矩阵乘法的Strassen算法</span></a></li></ol></li></ol>
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